Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing
DGMM 2022, IAPR Second International Conference on Discrete Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered...
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| Main Authors | , , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
28.07.2022
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2207.13926 |
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| Abstract | DGMM 2022, IAPR Second International Conference on Discrete
Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image processing, many dilations and erosions can be
written as the max-plus and min-plus product of a matrix on a vector. Previous
studies considered operators on symmetrical, unbounded complete lattices, such
as Cartesian powers of the completed real line. This paper focuses on
adjunctions on closed hypercubes, which are the complete lattices used in
practice to represent digital signals and images. We show that this constrains
the representing matrices to be doubly-0-astic and we characterise the
adjunctions that can be represented by them. A graph interpretation of the
defined operators naturally arises from the adjacency relationship encoded by
the matrices, as well as a max-plus spectral interpretation. |
|---|---|
| AbstractList | DGMM 2022, IAPR Second International Conference on Discrete
Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image processing, many dilations and erosions can be
written as the max-plus and min-plus product of a matrix on a vector. Previous
studies considered operators on symmetrical, unbounded complete lattices, such
as Cartesian powers of the completed real line. This paper focuses on
adjunctions on closed hypercubes, which are the complete lattices used in
practice to represent digital signals and images. We show that this constrains
the representing matrices to be doubly-0-astic and we characterise the
adjunctions that can be represented by them. A graph interpretation of the
defined operators naturally arises from the adjacency relationship encoded by
the matrices, as well as a max-plus spectral interpretation. |
| Author | Bloch, Isabelle Blusseau, Samy Angulo, Jesus Velasco-Forero, Santiago |
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| BackLink | https://doi.org/10.48550/arXiv.2207.13926$$DView paper in arXiv |
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| Snippet | DGMM 2022, IAPR Second International Conference on Discrete
Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image... |
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| SubjectTerms | Mathematics - Operator Algebras Mathematics - Representation Theory Mathematics - Spectral Theory |
| Title | Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing |
| URI | https://arxiv.org/abs/2207.13926 |
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